Computer simulation has become an indispensable tool in a wide variety of technical endeavors ranging from the design of aircraft, automobiles, and communications networks to the analysis of biological systems, socioeconomic trends, and plate tectonics. In the field of integrated circuit fabrication, computer simulation has become increasingly important as circuit line widths continue to shrink well below the wavelength of light. In particular, the optical projection of circuit patterns onto semiconductor wafers, during a process known as photolithography, becomes increasingly complicated to predict as pattern sizes shrink well below the wavelength of the light that is used to project the pattern. Historically, when circuit line widths were larger than the light wavelength, a desired circuit pattern was directly written to an optical mask, the mask was illuminated and projected toward the wafer, the circuit pattern was faithfully recorded in a layer of photoresist on the wafer, and, after chemical processing, the circuit pattern was faithfully realized in physical form on the wafer. However, for sub-wavelength circuit line widths, it becomes necessary to “correct” or pre-compensate the mask pattern in order for the desired circuit pattern to be properly recorded into the photoresist layer and/or for the proper physical form of the circuit pattern to appear on the wafer after chemical processing. Unfortunately, the required “corrections” or pre-compensations are themselves difficult to refine and, although there are some basic pre-compensation rules that a human designer can start with, the pre-compensation process is usually iterative (i.e., trial and error) and pattern-specific to the particular desired circuit pattern.
Because human refinement and physical trial-and-error quickly become prohibitively expensive, optical proximity correction (OPC) software tools have been developed for the automation (optionally with a certain amount of human analysis and interaction along the way) of pre-compensating a desired circuit pattern before it is physically written onto a mask. Starting with a desired circuit pattern, an initial mask design is generated using a set of pre-compensation rules. For the initial mask design, together with a set of process conditions for an actual photolithographic processing system (e.g., a set of illumination/projection conditions/assumptions for a “stepper,” a set of conditions/assumptions for the subsequent resist processing track, a set of conditions/assumptions for the subsequent etching process), a simulation is performed that generates simulated images of (i) the developed resist structure on the wafer that would appear after the resist processing track, and/or (ii) the etched wafer structure after the etching process. The simulated images are compared to the desired circuit pattern, and deviations from the desired circuit pattern are determined. The mask design is then modified based on the deviations, and the simulation is repeated for the modified mask design. Deviations from the desired circuit pattern are again determined, and so on, the mask design being iteratively modified until the simulated images agree with the desired circuit pattern to within an acceptable tolerance. The accuracy of the simulated images are, of course, crucial in obtaining OPC-generated mask designs that lead to acceptable results in the actual production stepper machines, resist processing tracks, and etching systems of the actual integrated circuit fabrication environments.
FIG. 1 illustrates a conceptual block diagram of a photolithographic processing system, which also serves as a general template for the way photolithographic process simulation systems are conceptually organized. It is to be appreciated, however, that the example of FIG. 1 is not presented by way of limitation, and that the various preferred simulation routines described hereinbelow can be aggregated or segregated in any of a variety of different ways without departing from the scope of the preferred embodiments. In the general process flow, a mask 104 (the terms “mask” and “photomask” are used interchangeably hereinbelow) based on a design intent 102 (arbitrarily chosen as an L-shaped feature for purposes of the present disclosure) is used by an optical exposure system 106 (e.g., a “stepper”) to expose a resist film 114 that disposed atop a wafer 116. The optical exposure system 106 comprises an illumination system 108 and a projection system 110. The illumination system 108 causes incident optical radiation to impinge upon the mask 104. The incident optical radiation is modulated by the mask 104 and projected onto the resist film 114. The optical exposure system 108 causes an optical intensity pattern 118 to be present in the resist film 114 during the exposure interval. A The exposed resist film 114 atop the wafer 116 is then processed by a resist processing system 120, such as by baking at a high temperature for a predetermined period of time and subjecting to one or more chemical solutions, to result in a developed resist structure 124. An etching process, such as a wet etching process or plasma etching process, is then applied by an etch system 126 to result in an etched wafer structure 130.
FIGS. 2A-2C illustrate conceptual diagrams of the optical intensity pattern 118, developed resist structure 124, and etched wafer structure 130 of FIG. 1, respectively, as broken out into discrete levels for facilitating clear presentation of the preferred embodiments. With reference to FIG. 2A, the optical intensity pattern 118 can be characterized as comprising “D” levels I(x,y,zl), l=1 . . . D, each level I(x,y,zl) being referenced as an optical intensity distribution 202. With reference to FIG. 2B, the developed resist structure 124 can be characterized as comprising “L” levels R(x,y,zn), n=1 . . . L, each level R(x,y,zn) being referenced as a developed resist distribution 206. With reference to FIG. 2C, the etched wafer structure 130 can be characterized as comprising “J” distinct levels W(x,y,zj), j=1 . . . J, each level W(x,y,zj) being referenced as an etched wafer distribution 210.
Notably, a typical thickness of the resist film 114 can be in the range of 100 30 nm-1000 nm and a desired height of the L-shaped feature on the etched wafer structure 130 can be hundreds of nanometers, while the desired line width of the L-shaped feature may be well under 100 nm (for example, 45 nm, 32 nm, and even 22 nm or below). In view of these very high aspect ratios, it becomes important for a simulation system to properly accommodate for the truly three-dimensional nature of the optical and chemical interactions that are taking place during the photolithographic process in order to be accurate. At same time, in view of the above-described iterative nature of the mask optimization process, it is desirable for the simulation results to be provided in a practicably short period of time, with increased ease of mask optimization being associated with faster computation times. Especially in view of the staggering amount of data associated with today's ever-shrinking and increasingly complex circuit patterns, there is a tension between providing sufficiently accurate simulations and providing sufficiently fast simulations.
While certain prior art approaches such as those based on differential-equation-solving techniques, finite difference techniques, or finite element techniques can provide accurate results, even to the extent of representing a kind of gold standard in their accuracy, they are generally quite slow. Approaches based on closed-form techniques avoid such timewise-recursive computation approaches and can therefore be much faster. However, many prior art closed-form techniques are believed to suffer from one or more shortcomings that are addressed by one or more of the preferred embodiments described hereinbelow. For example, many prior art closed-form techniques either ignore the third dimension altogether or are based on mathematical models do not adequately accommodate for the real-world, high aspect ratio, three-dimensional character of the interactions taking place. Other issues arise as would be apparent to one skilled in the art upon reading the present disclosure. By way of example, many known optical exposure system simulators operate on a simplifying assumption that the mask is a purely two-dimensional planar structure, whereas actual masks have some degree of thickness that affects the way the incident optical radiation is modulated. By way of further example, many of the above prior art techniques are unable to efficiently accommodate process variations in the photolithographic systems being modeled, and thus for each combination of values for physical variations in the photolithographic process (such as bake temperature, resist development time, etchant pH, stepper defocus parameter, etc.), such techniques require the entire (or almost entire) simulation process to be repeated essentially from the beginning. Provided in accordance with one or more of the preferred embodiments are methods, systems, and related computer program products for simulating a photolithographic processing system and/or for simulating a type or portion thereof such as an optical exposure system, a resist processing system, or etch processing system, in a manner that resolves one or more such shortcomings of the prior art. Although detailed herein primarily in terms of methods performed on described data, the scope of the preferred embodiments includes computer code stored on a computer-readable medium or in carrier wave format that performs the methods when operated by a computer, computer systems loaded and configured to operate according to the computer code, and generally any combination of hardware, firmware, and software mutually configured to operate according to the described methods.
According to one preferred embodiment, provided is a method for simulating a resist processing system according to a Wiener nonlinear model thereof, comprising receiving a plurality of precomputed optical intensity distributions corresponding to a respective plurality of distinct elevations in an optically exposed resist film, convolving each of the optical intensity distributions with each of a plurality of predetermined Wiener kernels to generate a plurality of convolution results, and cross-multiplying at least two of the convolution results to produce at least one cross-product. A first weighted summation of the plurality of convolution results and the at least one cross-product is computed using a respective first plurality of predetermined Wiener coefficients to generate a first Wiener output, and a resist processing system simulation result is generated based at least in part on the first Wiener output.
According to another preferred embodiment, provided is a method for calibrating a plurality of Wiener coefficients for use in a Wiener nonlinear model-based computer simulation of a resist processing system. First information representative of a reference developed resist structure associated with a test mask design is received. Second information is received representative of a plurality of precomputed optical intensity distributions corresponding to respective distinct elevations of an optical exposure pattern associated with the test mask design. Each of the optical intensity distributions is convolved with each of a plurality of predetermined Wiener kernels to generate a plurality of convolution results, and at least two of the convolution results are cross-multiplied to produce at least one cross-product. The plurality of Wiener coefficients are initialized. A current Wiener output is generated by computing a weighted summation of the plurality of convolution results and the at least one cross-product using the plurality of Wiener coefficients. The current Wiener coefficients are processed to generate third information representative of a current virtual developed resist structure, and the plurality of Wiener coefficients is modified based on the first information and the third information. The current Wiener output is then recomputed using the modified Wiener coefficients, and the process is repeated until a sufficiently small error condition is reached between the third information and the first information, at which point the latest version of the modified Wiener coefficients constitute the calibrated Wiener coefficients.
According to another preferred embodiment, provided is a method for simulating an etch system according to a Wiener nonlinear model thereof, comprising receiving a plurality of precomputed developed resist distributions corresponding to a respective plurality of distinct elevations in a developed resist structure, convolving each of the developed resist distributions with each of a plurality of predetermined Wiener kernels to generate a plurality of convolution results, and cross-multiplying at least two of the convolution results to produce at least one cross-product. A first weighted summation of the plurality of convolution results and the at least one cross-product is computed using a respective first plurality of predetermined Wiener coefficients to generate a first Wiener output, and an etch processing system simulation result is generated based at least in part on the first Wiener output.
According to another preferred embodiment, provided is a method for calibrating a plurality of Wiener coefficients for use in a Wiener nonlinear model-based computer simulation of an etch system. First information is received representative of a reference etched wafer structure associated with a precomputed test developed resist structure. Second information is received representative of a plurality of developed resist distributions corresponding to a respective plurality of distinct elevations in the precomputed test developed resist structure. Each of the developed resist distributions is convolved with each of a plurality of predetermined Wiener kernels to generate a plurality of convolution results, and at least two of the convolution results are cross-multiplied to produce at least one cross-product. The plurality of Wiener coefficients are initialized. A current Wiener output is generated by computing a weighted summation of the plurality of convolution results and the at least one cross-product using the plurality of Wiener coefficients, and the current Wiener output is processed to generate third information representative of a current virtual etched wafer structure. The current Wiener output is then recomputed using the modified Wiener coefficients, and the process is repeated until a sufficiently small error condition is reached between the third information and the first information, at which point the latest version of the modified Wiener coefficients constitute the calibrated Wiener coefficients.
According to another preferred embodiment, provided is a method for simulating an optical exposure system in which optical radiation incident upon a photomask is modulated thereby and projected toward a target to generate a target intensity pattern, the optical radiation incident upon the photomask comprising a plurality of spatial frequency components. First information representative of a first of the plurality of spatial frequency components is received. Each of the mask layer distribution functions is convolved with each of a plurality of predetermined Wiener kernels to generate a plurality of convolution results, and at least two of the convolution results are cross-multiplied to produce at least one cross-product. A first Wiener output representative of a first modulated radiation result associated with the first spatial frequency component is computed as a weighted summation of the plurality of convolution results and the at least one cross-product using a respective first plurality of predetermined Wiener coefficients, and a target intensity pattern is generated based at least in part on the first modulated radiation result.
According to another preferred embodiment, provided is a method for calibrating a plurality of Wiener coefficients for use in a Wiener nonlinear model-based computer simulation of photomask diffraction of incident optical radiation at a selected spatial frequency. First information representative of a reference modulated radiation result associated with a test photomask and the selected spatial frequency is received. A plurality of mask layer distribution functions representative of a respective plurality of layers of the test photomask is received. Each of the mask layer distribution functions is convolved with each of a plurality of predetermined Wiener kernels to generate a plurality of convolution results, and at least two of the convolution results are cross-multiplied to produce at least one cross-product. The plurality of Wiener coefficients is initialized. A current Wiener output representative of a current virtual modulated radiation result is generated as a weighted summation of the plurality of convolution results and the at least one cross-product using the plurality of Wiener coefficients. The plurality of Wiener coefficients is modified based on the reference modulated radiation result and the current virtual modulated radiation result. The current Wiener output is then recomputed using the modified Wiener coefficients, and the process is repeated until a sufficiently small error condition is reached between the current modulated radiation result and the reference modulated radiation result, at which point the latest version of the modified Wiener coefficients constitute the calibrated Wiener coefficients.
According to another preferred embodiment, provided is a method for simulating a resist processing system that undergoes process variations characterized by a plurality of process variation factors according to a Wiener nonlinear model thereof. A plurality of precomputed optical intensity distributions is received corresponding to a respective plurality of distinct elevations in an optically exposed resist film. Each of the optical intensity distributions is convolved with each of a plurality of predetermined Wiener kernels to generate a plurality of convolution results, and at least two of the convolution results are cross-multiplied to produce at least one cross-product. Values for the plurality of process variation factors are received. Each of a plurality of Wiener coefficients is computed as a respective predetermined polynomial function of the process variation factors characterized by a respective distinct set of predetermined polynomial coefficients. A Wiener output is generated as a weighted summation of the plurality of convolution results and the at least one cross-product using the computed plurality of Wiener coefficients, and a resist processing system simulation is generated based at least in part on the Wiener output.
According to another preferred embodiment, provided is a method for calibrating a plurality of sets of polynomial coefficients for use in a Wiener nonlinear model-based computer simulation of a resist processing system, the resist processing system undergoing process variations characterized by a plurality of process variation factors. First information is received representative of a plurality of reference developed resist structures, the reference developed resist structures being associated with a common test mask design but each being associated with a respective one of a known plurality of distinctly valued process variation factor sets associated with the resist processing system. Second information is received representative of a plurality of precomputed optical intensity distributions corresponding to respective distinct elevations of an optical exposure pattern associated with the common test mask design. Each of the optical intensity distributions is convolved with each of a plurality of predetermined Wiener kernels to generate a plurality of convolution results, and at least two of the convolution results are cross-multiplied to produce at least one cross-product. The plurality of sets of polynomial coefficients is initialized. A plurality of current Wiener outputs associated with respective ones of the distinctly valued process variation factor sets is computed, wherein, for each distinctly valued process variation factor set, computing the current Wiener output comprises (i) computing each of a plurality of Wiener coefficients as a respective predetermined polynomial function of the process variation factors, each predetermined polynomial function using a respective one of the sets of polynomial coefficients, and (ii) generating the current Wiener output as a weighted summation of the plurality of convolution results and the at least one cross-product using the computed plurality of Wiener coefficients. The plurality of current Wiener outputs is processed to generate third information representative of a respective plurality of current virtual developed resist structures, and each of the plurality of sets of polynomial coefficients is modified based on the first information and the third information. The plurality of current Wiener outputs is then recomputed using the plurality of modified sets of polynomial coefficients, and the process is repeated until a sufficiently small error condition is reached between the third information and the first information, at which point the latest version of the plurality of modified sets of polynomial coefficients constitutes the calibrated plurality of sets of polynomial coefficients.